In this paper, we present a novel method for solving FRACTIONAL Transportation Problems (FTPs) with FUZZY numbers using a ranking function. The proposed method introduces a transformation technique that converts an FTP with FUZZY numbers into an FTP with crisp numbers by employing the robust ranking technique. Subsequently, we formulate two transportation problems, one for maximization and another for minimization, based on the given FTP. The optimal solution for the original FTP is then derived by leveraging the solutions obtained for the formulated transportation problems. By optimizing these single-objective transport problems, our method provides decision-makers with the ability to make satisfactory managerial decisions and evaluate economic operations when confronted with logistic problems involving FRACTIONAL transportation. To demonstrate the effectiveness of the proposed approach, we present several illustrative examples that showcase its practical application and efficiency.

We develop an algorithm for the solution of multiobjective LINEAR plus FRACTIONAL PROGRAMMING problem (MOL+FPP) when some of the constraints are homogeneous in nature. Using homogeneous constraints, first we construct a transformation matrix T which transforms the given problem into another MOL+FPP with fewer constraints. Then, a relationship between these two problems, ensuring that the solution of the original problem can be recovered from the solution of the transformed problem, is established. We repeat this process of transformation until all the homogeneous constraints are removed. Then, we discuss the multi objective PROGRAMMING part, for which FUZZY PROGRAMMING methodology is proposed which works for the minimization of perpendicular distances between two hyper planes (curves) at the optimal points of the objective functions. A suitable membership function is defined with the help of the supremum perpendicular distance. A compromised optimal solution is obtained as a result of the minimization of the The supremum perpendicular distance. The corresponding optimal solution to the original problem is obtained using the transformation matrix. Finally, an example is given to illustrate the proposed model.

In this paper a multi-objective LINEAR FRACTIONAL PROGRAMMING problem with the FUZZY variables and vector of FUZZY resources is studied and an algorithm based on a parametric approach is proposed. The proposed solving procedure is based on the parametric approach to find the solution, which provides the decision maker with more complete information in line with reality. The simplicity of the proposed method is one of the advantages of the presented algorithm, which allows the decision maker to better understand the solving procedure. Moreover, a numerical example is presented to illustrate the proposed method.